**Modeling decimal multiplication :**

For some real-world problems, we may need to multiply two decimals.

Let us see how decimal multiplication can be modeled through some examples.

**Example 1 : **

Multiply 0.3 and 0.5.

**Solution :**

To multiply 0.3 and 0.5, let us consider decimal grids given below.

0.3 × 0.5 represents 0.3 of 0.5.

Shade 5 rows of the decimal grid in green color to represent 0.5

Shade 3 columns of the decimal grid in red color to represent 0.3

Now shade the common region of 0.5 and 0.3 in blue color.

In the common region of 0.5 and 0.3 in blue color, there are 15 squares.

This represents 15 hundredths or 0.15.

Therefore, 0.3 x 0.5 = 0.15

**Example 2 : **

Multiply 3.2 and 2.1

**Solution :**

Let us use area model to multiply 3.2 and 2.1.

In this model, the large squares represent wholes, the small rectangles along the right and lower edges represent tenths, and the small squares at the lower right represent hundredths.

This model is 3 and 2 tenths units long, and 2 and 1 tenth units wide.

The area of the model is

**6 wholes + 7 tenths + 2 hundredths** sq. units

Therefore, 3.2 x 2.1 = 6.72

**Problem 1 : **

Multiply 2.3 and 1.78

**Solution :**

Imagine the given decimals as whole numbers.

Then, we have 23 and 178.

Now, multiply 23 and 178.

23 x 178 = 4094

In the first decimal 2.3, there is one digit after the decimal point and in 1.78, there are two digits after the decimal point.

So, we have

1 + 2 = 3

In the above result 4094, there must be 3 digits after the decimal.

Hence, 2.3 x 1.78 = 4.094

**Problem 2 :**

The side of a square is 3.2 cm. Find its perimeter.

**Solution :**

All the sides of a square are equal.

Length of each side = 3.2 cm.

Perimeter of a square = 4 × side

Thus, perimeter = 4 × 3.2 = 12.8 cm.

**Problem 3 :**

The length of a rectangle is 6.3 cm and its breadth is 3.2 cm. What is the area of the rectangle?

**Solution :**

Length of the rectangle = 6.3 cm

Breadth of the rectangle = 3.2 cm.

Area of the rectangle = ( length) × (breath)

= 6.3 × 3.2

= 20.16 cm²

**Problem 4 :**

Multiply 3.723 by 100

**Solution :**

We multiply by 3.723 by 100. So, we have to move the decimal point two digits to the right.

3.723 x 100 = 372.3

Multiplying 3.723 by 100, we get 372.3

**Problem 5 :**

Multiply 3.723 by 1000

**Solution :**

We multiply by 3.723 by 1000. So, we have to move the decimal point two digits to the right.

3.723 x 1000 = 3723

Multiplying 3.723 by 1000, we get 3723

**Problem 6 :**

The price of a fruit is $3.52 per lb. Find the cost of 10 lbs of fruits.

**Solution :**

Given : Cost of 1 lb of fruit = $3.52

Then, the cost of 10 lbs of fruits is

= 10 x 3.52

We multiply by 3.52 by 10. So, we have to move the decimal point one digit to the right.

So, we get

= 35.2

Hence, the cost of 10 lbs of fruits is $35.2

**Problem 7 :**

A person walks regularly in the morning. If the speed of his walking is 43.26 ft per minute, Find the distance covered by him in 100 minutes.

**Solution :**

Given : Speed is 43.26 ft per minute.

So, distance covered in one minute is 43.26 ft.

We all know the formula for distance.

That is,

Distance = Speed x Time

To know the distance covered in 100 minutes, we have to plug time = 100 and the speed is 43.26

Distance = 43.26 x 100

We multiply by 43.26 by 100. So, we have to move the decimal point two digits to the right.

So, we get

Distance = 4326 ft

Hence, the distance covered by him in 100 minutes is 4326 ft.

**Problem 8 :**

One-thousandth of a certain number is 0.003. What is the number?

**Solution :**

Given : One-thousandth of a certain number is 0.003

Let "a" be the number.

Then, from the given information, we get

(1/1000) x a = 0.003

Multiplying by 1000 on both sides, we get

a = 0.003 x 1000

We multiply by 0.003 by 1000. So, we have to move the decimal point three digits to the right.

So, we get

a = 3

Hence, the the number is 3.

After having gone through the stuff given above, we hope that the students would have understood "Modeling decimal multiplication".

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